arXiv subjects

Yoonkyeong Lee

Publications and source records attributed to Yoonkyeong Lee.

4 recordsLinked to original sources

arXiv2026

Irreducibility and weak spectral gap in free product von Neumann algebras

Consider a free product $(M,φ)= (M_1,φ_1)* (M_2,φ_2)$ of non-trivial von Neumann algebras. Using amalgamated free product techniques, we establish irreducibility and weak spectral gap results for free product subalgebras and the centralizer subalgebra of the free product state. In particular, it is shown that, under a mild dimension constraint, the inclusion of the diffuse summand of these subalgebras into the corresponding corner of $M^ω$ is irreducible for any free ultrafilter $ω\in β\mathbb{N}\setminus \mathbb{N}$. We also obtain analogous irreducibility results for graph products of von Neumann algebras.

math.OA↗

arXiv2026

Strong convergence to operator-valued semicirculars

We establish a framework for weak and strong convergence of matrix models to operator-valued semicircular systems parametrized by operator-valued covariance matrices $η= (η_{i,j})_{i,j \in I}$. Non-commutative polynomials are replaced by covariance polynomials that can involve iterated applications of $η_{i,j}$, leading to the notion of covariance laws. We give sufficient conditions for weak and strong convergence of general Gaussian random matrices and deterministic matrices to a $B$-valued semicircular family and generators of the base algebra $B$. In particular, we obtain operator-valued strong convergence for continuously weighted Gaussian Wigner matrices, such as Gaussian band matrices with a continuous cutoff, and we construct natural strongly convergent matrix models for interpolated free group factors.

math.OA↗

arXiv2025

On conjugate systems with respect to completely positive maps

We study the operator-valued partial derivative associated with covariance matrices on a von Neumann algebra B. We provide a cumulant characterization for the existence of conjugate variables and study some structure implications of their existence. Namely, we show that the center of the von Neumann algebra generated by B and its relative commutant is the center of B.

math.OA↗

arXiv2025

On the genericity of irreducible subfactors

We show that finitely generated irreducible $\mathrm{II}_1$ subfactors are generic in the following sense. Given a separable $\mathrm{II}_1$ factor $M$ and an integer $n\geq 2$, equip the set of $n$-tuples of self-adjoint operators in $M$ with norm at most $1$ with the metric $d(x,y) = \max_{1\leq i \leq n} \|x_i - y_i\|_2$. Then the set of $n$-tuples that generate an irreducible subfactor of $M$ forms a dense $G_δ$ set in this metric space. On the way to proving this result, we show that closable derivations vanish on the anticoarse space associated to their kernels, which leads to new applications of conjugate systems in free probability.

math.OA↗